This invention relates to nuclear magnetic resonance imaging methods and systems and, more particularly, to acquisition of images using spiral scanning methods.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field along a longitudinal z axis, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment M.sub.z may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A nuclear magnetic resonance (NMR) signal is emitted by the excited spins after the excitation signal B.sub.1 is terminated, and may be received and processed to form an image.
When utilizing NMR signals to produce images, magnetic field gradients (G.sub.x G.sub.y and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used to sample a two or three dimensional region of k-space. The resulting set of received k-space signals is digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
Most magnetic resonance (MR) scans currently used to produce medical images require many minutes to acquire the necessary k-space data. Reducing this scan time is an important objective, since a shortened scan increases patient throughput, improves patient comfort, and improves image quality by reducing motion artifacts. Reduction of scan time is particularly important in cardiac imaging, for example, where it is highly desirable to acquire sufficient NMR data to reconstruct an image in a single breath hold.
Many different pulse sequences are known in the art for acquiring NMR signals from which an image may be reconstructed. Most of these pulse sequences sample k-space in a rectilinear pattern, but there is a class of pulse sequences which sample k-space in a spiral pattern. It is known that a spiral sampling pattern can be achieved by applying a sinusoidally varying readout magnetic field gradient during acquisition of each NMR signal and that spiral scanning methods can be used to rapidly acquire NMR data from which an image may be reconstructed. A spiral scanning method is also known wherein the sinusoidal readout gradient is shaped to more rapidly traverse the spiral sampling trajectory and, therefore, more rapidly sample k-space data. Scan time has been further reduced in the past by acquiring samples from only one-half of k-space using interleaved spiral sampling trajectories.
Prior spiral trajectory k-space sampling methods are derived from Archimedian spirals of the form: EQU k.sub.x (t)=a(t)cos[a(t)] EQU k.sub.y (t)=a(t)sin[a(t)].
Given the amplitude and slew rate limitations of the gradient system hardware, the function a(t) is determined numerically such that k-space is sampled in a minimum scan time. While sampling with an Archimedian spiral trajectory allows very short scan times, the sampling of k-space is not uniform. The sampling is more dense near the center of k-space, with the result that the peripheral regions are undersampled if the central region is sampled at a rate needed to satisfy the Nyquist criteria. Such undersampling produces a variety of image artifacts in the reconstructed image.